基于p范数的QR-KPCA人脸识别算法

摘要

K PC A是重要的非线性特征提取的人脸识别方法，但对较大规模训练数据库，会因核矩阵 K过大，计算代价高而不能有效实现，并且使用传统欧式距离度量很难大幅提升识别率。本研究提出了将基于QR分解的PCA推广到KPCA上且应用 p范数度量来解决这一问题的方法，即：首先采用选主元的Cholesky分解得到核矩阵K的低秩近似，然后对小规模矩阵 H进行QR分解，经过一些推导得到中心化核矩阵的特征向量，实现了KPCA的非线性特征提取，在分类识别阶段，本研究突破传统欧氏距离度量的局限，将 p范数作为度量相似性的方法，在O RL和A R人脸数据库中做了大量相关实验，并且分别研究了 p的取值对基于QR分解的主成分分析（QR‐PCA ）和核主成分分析（QR‐KPCA）算法的识别率的影响，实验结果表明，这种 p范数意义下的QR‐KPCA处理人脸识别问题有很高的识别率。%KPCA is an important human face recognition method for the non‐linear feature extrac‐tion .But it cannot effectively realize the large‐scale training data bank for kernel matrix is too large and calculation cost is too high ,and the use of traditional Euclidean distance metric is diffi‐cult to raise recognition rate by a large margin .This research suggests that PCA base on QR de‐composition be extended to KPCA and that p norm measurement be used to solve this problem . First of all ,the main element Cholesky decomposition is selected to obtain the low rank approxi‐mation of kernel matrix K ,and then ,small‐scale matrix H is to carry out QR decomposition . Through some deductions ,the eigenvectors of centralized kernel matrix can be obtained so as to realize KPCA non‐linear feature extraction . In the classification recognition stage , a break‐through is made in the restriction by the traditional Euclidean distance metric ,and the p norm can be used as the method to measure the similarity in this research .A large number of experiments have been conducted in ORL and AR human face data bank .Also ,a study is made of p value tak‐ing to the principal components analysis(QR‐PCA) based on QR decomposition and effect on QR‐KPCA Algorithm recognition rate .The experiments results indicate that the QR‐KPCA treat‐ment of human face recognition problem is of very high recognition rate under this p norm signifi‐cance .